Position location systems are used to provide location identification support for location-sensitive services and applications. Examples of location-sensitive services and applications include asset management, service personnel tracking, delivery vehicle tracking, and package or shipment tracking. In the case of critical asset tracking, organizations such as defense contractors have a need to track parts and equipment of a sensitive, secure, and hazardous nature, such that movements are recorded to provide some indication of who has had access to them, and as proof that they have not been tampered with or viewed by unauthorized personnel. Other examples of location-sensitive services and applications include roadside assistance, boundary maintenance, driving directions, caller location tracking, and fixed asset location monitoring. Vehicle location tracking may be used to enable dispatchers to monitor delivery vehicle location without driver intervention. Public safety services like the provision of 112 and 911 services also have a need for location tracking. Phase I of the US Federal Communications Commission's (“FCC”) E911 rules requires that wireless operators provide to Public Safety Answering Points (“PSAP”) with the mobile number of each wireless 911 call, allowing the PSAP dispatcher to attempt to call back to the mobile device if the call is disconnected or to obtain additional information. Phase I also requires mobile device operators to provide to PSAPs the location of the cell site that handled the origination of each 911 call. Both the call-back number and the cell site location are to be transmitted by the mobile device so that they arrive at the PSAP at approximately the same time as the call. Phase II of the FCC's wireless E911 rules requires mobile devices to provide to PSAPs the calling number and the caller's physical location within an average distance tolerance of about 100 meters. Other uses for location tracking include security applications where authorities may want to be able to track the locations of probationers, child locators where parents want to be able to track the whereabouts of their children, and general service locators where mobile consumers may want to be able to determine “Where is the nearest ABM to where I am currently located?” or “How far away is the nearest MacDonald's Restaurant?” or “What are the traffic conditions in my vicinity?” Location may also be useful in wireless sensor networks which require sensor nodes to know their physical locations, such as target detection and tracking, precision navigation and, search and rescue, geographic routing, and security surveillance. Further, knowledge of sensor location can be used to facilitate network functions such as packet routing, and collaborative signal processing. Sensor position can also serve as a unique node identifier, making it unnecessary for each sensor to have a unique ID assigned prior to its deployment.
Driven by the demand for location detection and tracking systems, many techniques have been proposed in recent years. Perhaps the most popular location detection techniques include received-signal-strength-indicator (“RSSI”), angle-of-arrival (“AOA”), time-of-arrival (“TOA”), and time-difference-of-arrival (“TDOA”). Many of these techniques operate in two phases: a range or angle measurement phase, and position calculation phase where the measurements are transformed into a position estimate. Some techniques perform a pre-processing and/or refinement phase before/after generating and initial estimate. However, each of these techniques has drawbacks. The angle of arrival and received signal strength, for example, provide only a relatively coarse indication of angle and proximity, and can be affected by extraneous factors such as reflections and attenuation by intervening objects. Time of arrival is sometimes impractical because it requires precise time synchronization of all involved fixed and mobile devices. Further, the accuracy of the location calculation is a function of the accuracy of the time synchronization. In the case of round trip time of flight, only the measuring devices require precise time synchronization. However, the measuring devices require precise delay/processing time data for each response. Time-difference-of-arrival requires only the precise time synchronization of the measurement devices. However, the locations of the measuring devices must be known with precision for forming and solving elliptical equations.